Fun with Math!: Polar

Friday, January 13, 2012

A coordinate (x,y) in xy-plane can be written in polar form $(r,\theta)$ , where r is the directed distance from (0,0) to (x, y), and $\theta$ is the directed angle formed by the vector $\left \langle x,y \right \rangle$ ; from the positive side of x-axis, where
$r=\pm \sqrt{x^2 + y^2}$
$\theta=\tan^{-1} \frac{y}{x}$

You may try to drag the value of the sliders in the graph to look at Point A and the coordinates in $(x,y)$ and $(r,\theta)$ . Take note that the value of $\theta$ is in radian mode.

There are some interesting graphs can be obtained through polar equations, such as